A time series is a sequence of observations collected through time. Time series data are regularly collected in many fields, including economics, finance and environmental sciences. This course will focus on the fundamental concepts required for the description, modelling and forecasting of time series data. An introduction to the theoretical foundation of time series models will also be provided. Topics to be covered include: descriptive methods, linear and non-linear time series models, tools for model identification and estimation, and spectral analysis.
The revision class (for both Time Series and Monte Carlo Inference) will take place in MR5 from 1400-1600 on 13 May 2015 (Wednesday). We will disucss last year's examination paper, which can be found here.
This course consists of 12 lectures. It is the first half of the Part III course Time Series and Monte Carlo Inference. Students who take this course must also take the second half Monte Carlo Inference for the examination.
The official syllabus of this course can be found here.
The proofs are not included in the slides or summaries.
Other (more general) topics covered in this course include correlation and causation, and regression to the mean.
- Example Sheet 1 and its Solutions
- Example Sheet 2 (updated) and its Solutions (corrected)
- If you are completely new to R, I suggest having a quick look at R for Beginners first.
- Prof. David Stoffer has a nice R tutorial on time series analysis, which can be found here.
- Introduction to Time Series and Forecasting (by P. J. Brockwell and R. A. Davis) serves as a good introduction, especially for those completely new to time series analysis.
- Time Series: Applications to Finance with R and S-Plus (by N. H. Chan) covers large parts of this course, presented in a less mathematical and very concise style. Its electronic resource is available here through the publisher's website. Your Cambridge Hermes account is required if you want to view it from outside the campus.
- Time Series Analysis and its Applications: with R Examples (by R. H. Shummway and D. S. Stoffer) is another great book on time series analysis aimed at roughly the same level as our course. The first four chapters of this book are kindly made available by the authors. They can be freely accessed from here.
- GARCH Models: Structure, Statistical Inference and Financial Applications (by C. Francq and J-M. Zakoian) is an excellent read for those who are keen to know more about non-linear time series models. It provides a comprehensive and systematic approach to understanding GARCH time series models from a mathematical (theoretical) perspective. Its electronic resource is available here through the publisher's website. Your Cambridge Hermes account is needed if you want to view it from home.
- Time Series: Theory and Methods (by P. J. Brockwell and R. A. Davis) covers the first part of our course (linear time series models) in much greater depth than we do. It also contains rigorous proofs of many theoretical results that we state but do not prove in the lectures. (NB. most of these proofs are contained in its Chapters 6-8, which can be a hard read for those new to time series.)
Prof. Richard Weber taught this course in 2001. You may find his lecture notes helpful.
Prof. Robert Gramacy taught this course in 2010. He made some interesting R demos, which can be found here.
NB. Topics on non-linear time series models (such as ARCH and GARCH) are not covered in the above-mentioned sources.
If you have any comments and/or questions about this course, you can send them to me (anonymously if you wish) using the form below. In particular,
- if you feel that I go too fast or too slowly
- or if there are parts of the lectures you do not understand,
please let me know so that I can make adjustments accordingly in the next lecture.
Yining Chen, last update: 4 Feb 2015